Help to formally write down a linear regression

[renato25]

Hello altogether,

i am currently analysing a dataset of 10,000 transactions. I am analysing the effect of different advertising campaings on the quantity of chairs by using multiple linear regression model with zip code and day dummies. I am interested in formally writing the regression model down and wanted to ask if you think it is okay in the following way:

Yi = ß0 + ß1 * Ti + ß2 * Xi + ß3 * di + ei

Yi = quantity of chairs
i = specific transaction
Ti = a set of dummy variables that indicates which add the customer of the transaction saw
Xi = Dummy for the zip code to which the products where shipped
Di = Dummy for the date of the transaction
ei = error term

It would really help to know if it is okay. I have some problems with my output and wanted to start at the basiscs.

Best regards
Renato

 

[hlsmith]

You model has many more terms than listed above. It works for basic explanation, but I think you need to have some additional subscripts and ellipses, to hold the place for all of the dummies.

 

[renato25]

Thank you for your reply hlsmith. I added an apostrophe to indicate that the T, X and d are dummy variables. So my new equation is:
Yi = ß0 + ß1 * T'i + ß2 * X'i + ß3 * d'i + ei

Alternatively I can write dti, where t is the subscript for the specific day and i the subscript for the specific transaction. The same for Ti and Xi.

Is that what you meant?

Thank you very much. I really think this basic work helps me.

 

[Dason]

Your equation still implies that there are only four parameters being estimated. You need to make it clear that each dummy variable is getting its own parameter as well.

 

[renato25]

Thank you Dason. You are right. Of course there is a ß1 for each T included. I looked through some papers and some of them just write it with an apostrophe like this:
Yi = ß0 + a' * T'i + z' * X'i + o' * d'i + ei

So a' is a vector for the different parameters that are estimated. The same holds true for z' and o'. Is it okay to write it like this?

And what to do woth the constant? Most of the papers I looked at leave it out but there is one constant for each customer so that ß0 is correct, right? Or what would be correct?

Again, thank you very much for your patience and time.